指数抽样分布定理及三个期望之极小方差无偏估计的有效性比较
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摘要
在相关文献工作的基础上完善指数抽样分布定理.首先导出指数分布样本最大值与样本最小值之差的分布,并证明了样本最大值与样本最小值之差和样本最小值相互独立;然后导出指数分布样本最大值与样本均值之差的分布,并证明了样本最大值与样本均值之差和样本最小值相互独立.从而构造出三个期望之极小方差无偏估计,基于样本均值与样本最小值之差和样本最小值构造出的期望之极小方差无偏估计,恰好是期望之一致最小方差无偏估计;文末,在小样本情景下,对上述三个期望之极小方差无偏估计作了有效性比较.
This article continues the works of references,so as to improve and perfect the exponential sample theorem.first,the distribution of the difference between sample maximum and minimum of exponential distribution is derived,and that the difference of these two statistics is mutually independent with the sample minimum is proven.Also,this article derives the distribution of the difference between sample maximum and sample mean,and demonstrates that the difference of these two statistics is mutually independent with the sample minimum.Thus,the three local minimum variance unbiased estimators could be built,the one which is built by sample minimum and the difference between sample mean and sample minimum,is precisely the UMVUE of of mean of the Exponential distribution.At last,in small sample,the efficiency comparison is made among above-mentioned three local minimum variance unbiased estimators of mean of the Exponential distribution.
This article continues the works of references,so as to improve and perfect the exponential sample theorem.first,the distribution of the difference between sample maximum and minimum of exponential distribution is derived,and that the difference of these two statistics is mutually independent with the sample minimum is proven.Also,this article derives the distribution of the difference between sample maximum and sample mean,and demonstrates that the difference of these two statistics is mutually independent with the sample minimum.Thus,the three local minimum variance unbiased estimators could be built,the one which is built by sample minimum and the difference between sample mean and sample minimum,is precisely the UMVUE of of mean of the Exponential distribution.At last,in small sample,the efficiency comparison is made among above-mentioned three local minimum variance unbiased estimators of mean of the Exponential distribution.
引文
[1]李国安.指数分布抽样基本定理及在四参数二元Marshall-Olkin型指数分布参数估计中的应用[J].统计研究,2016,33(7):98-102.
[2]李国安,李建峰.指数分布抽样基本定理及在三参数一般指数分布参数估计中的应用[J].数学的实践与认识,2017,47(3):165-169.
[3]Lawrance A J,Lewis P A W.Simple dependent pairs of exponential and uniform random variables[J].Operations Research,1983,31:1179-1197.
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[6]Al-Saleh M F,Al-Hadhrami S A.Estimation of the mean of the exponential distribution using moving extremes ranked set sampling[J].Statistical Papers,2003,44:367-382.
[7]Baklizi A,Dayyeh W A.Shrinkage Estimation of P(Y [8]Dixit U J,Nasiri P N.Estimation of parameters of a right truncated exponential distribution[J].Statistical Papers,2008,49:225-236.
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[10]Kundu D,Gupta R D.Bivariate generalized exponential distributions[J].Journal of Multivariate Analysis,2009,100:581-593.
[11]Marshall A W,Olkin I.A multivariate exponential distribution[J].Journal of American Statistical Association,1967,62(1):30-44.
[12]Arnold B C.Parameter estimation for a multivariate exponential distribution[J].Journal of American Statistical Association,1968,63:848-852.
[2]李国安,李建峰.指数分布抽样基本定理及在三参数一般指数分布参数估计中的应用[J].数学的实践与认识,2017,47(3):165-169.
[3]Lawrance A J,Lewis P A W.Simple dependent pairs of exponential and uniform random variables[J].Operations Research,1983,31:1179-1197.
[4]Cohen A C,Helm E R.Estimation in the Exponential Distribution[J].Technometrics,1973,15(2):415-418.
[5]Nie K,Sinha B K,Hedayat A S.Unbiased estimation of reliability function from a mixture of two exponential distributions based on a single observation[J].Statistics and Probability Letters,2017,127-713.
[6]Al-Saleh M F,Al-Hadhrami S A.Estimation of the mean of the exponential distribution using moving extremes ranked set sampling[J].Statistical Papers,2003,44:367-382.
[7]Baklizi A,Dayyeh W A.Shrinkage Estimation of P(Y
[9]Gupta R D,Kundu D.Generalized exponential distributions[J].Australian and New Zealand Journal of Statistics,1999,41:173-188.
[10]Kundu D,Gupta R D.Bivariate generalized exponential distributions[J].Journal of Multivariate Analysis,2009,100:581-593.
[11]Marshall A W,Olkin I.A multivariate exponential distribution[J].Journal of American Statistical Association,1967,62(1):30-44.
[12]Arnold B C.Parameter estimation for a multivariate exponential distribution[J].Journal of American Statistical Association,1968,63:848-852.